Industry generally calls for composite materials consisting of a polymer matrix whose properties, in particular the mechanical properties, must be adapted by incorporation of fillers or reinforcements. Certain of these composite materials are produced from copolymer latexes and fibers. These are the materials to which the present invention relates. With regard to reinforcement, the advantage of cellulose, in particular particles of microcrystalline cellulose, has already been recognized, for the reinforcement of polymers from using their solutions, for example, the aqueous solutions of carbamide resins mentioned in WO 93/10172, or else for the production of compositions for nail polishes (U.S. Pat. No. 4,891,213) of which the secondary but important properties such as transparency or luster of the composite have been assessed. Also envisaged has been the filling or reinforcing with cellulose by the ordinary methods of compounding of thermoplastic resins (for examples see: Composite Systems from Natural and Synthetic Polymers, by Kalson et al. in Materials Science Monographs, 36, Elsevier 1986, or else Future Prospects for Wood Cellulose as Reinforcement in Organic Polymer Composites, by Zadorecki et al. in Polymer Composites, 10/2, p. 69, 1989).